34 On the Action of the Second Surfaces, fyc. 



Let us now apply the results of the preceding analysis to M. 

 Arago's experiment shown, in Fig. 1. Suppose the angle of inci- 

 dence to be 78° 1', and let the light polarized by reflexion at A (Fig. 

 3.)be=w2, and that polarized by one refraction also=m. Then 

 smce the pencil 6 5 is common light, the polarized light in the whole 

 reflected pencil AV,hs is=m, whereas the light polarized by the 

 two refractions is=^2m ; so that M. Arago's experiment makes two 

 quantities appear equal when the one is double that of the other. 

 If the angle exceeds 78° 1', the oppositely polarized light in the pen- 

 cil 6s will neutralize a portion of the polarized light in the pencil 

 AP, and the ratio of the oppositely polarized rays which seem to be 

 compensated in the experiment, may be that of 3 m or even 4 m to 1. 



Having thus determined the changes- which light undergoes by 

 reflexion from plates, it is easy to obtain forraulce for computing the 

 exact quantities of polarized light at any angle of incidence, either 

 in the pencil C B S or 6 5. 



The primitiv^e ray RA being common light, AC will not be in that 

 state, but will have its planes of polarization turned round a quantity 

 X by the refraction at A; so that cota;= cos(i — i'). Hence we must 

 adopt for the measure of the light reflected at C the formula of Fres- 

 nel for polarized liglit whose plane of incidence forms an angle x with 

 the plane of reflexion. The intensity of AC being known from the for- 

 mula for common light, we shall call it unity, then the intensity I of the 

 two pencils polarized —x and -\-x to the plane of reflexion will be 

 s\n~{i — i') tan-(z — «■') 



sm^{i-f-i) tan- («-{-*) 



cos(^-|-^^) 



+ 1 



\ , , / cos(i-f ^) \ 2/ 



\{cos[i— i') )^ . 

 In like manner if we call the intensity of CB = ], we shall have 



cos{i-{-t\ 



Tan a: — t y-- — ^Tw 



(cos(^— i'^))-^ 



and the intensity I of the transmitted pencil b s 



sia^(i— i') tan-(z — i') . 



1 = 1 — • „■/• I v\ C0S"a;-l-- — r-v- , ..x Sin-.r and 

 sm-(i -(-»') tan^(^-f-^) 



[cos{i — i') )'■ 

 ^"^\ cos{i+i') I 



